Algebra 1A: Unit 3 Linear Functions Test

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis. It is the value of y when x = 0.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then, shade the region that satisfies the inequality.

Front

What does the inequality x + 4y ≤ -20 represent graphically?

Back

The inequality x + 4y ≤ -20 represents a region on the coordinate plane that includes all points (x, y) that satisfy the condition. The boundary line is x + 4y = -20.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients in a linear equation determine the slope and the y-intercept of the line. The coefficient of x is the slope, and the constant term is the y-intercept.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the graphs of the equations intersect.